An efficient method for evaluating energy-dependent sum rules

Abstract

Energy-dependent sum rules are useful tools in many fields of physics. In nuclear physics, they typically involve an integration of the response function over the nuclear spectrum with a weight function composed of integer powers of the energy. More complicated weight functions are also encountered, e.g., in nuclear polarization corrections of atomic spectra. Using the Lorentz integral transform method and the Lanczos algorithm, we derive a computationally efficient technique for evaluating such sum rules that avoids the explicit calculation of both the continuum states and the response function itself. Our numerical results for electric dipole sum rules of the Helium-4 nucleus with various energy-dependent weights show rapid convergence with respect to the number of Lanczos steps. This demonstrates the usefulness of the method in a variety of electroweak reactions.

7 pages, 2 figures, 1 table

References in corpus (5)

• Chiral effective field theory and nuclear forces
• Local three-nucleon interaction from chiral effective field theory
• The Lorentz Integral Transform (LIT) method and its applications to perturbation induced reactions
• Sum rules, dipole oscillation and spin polarizability of a spin-orbit coupled quantum gas
• Photonuclear sum rules and the tetrahedral configuration of ${}^4$He

Cited by in corpus (4)

• Giant and pigmy dipole resonances in 4He, 16,22O, and 40Ca from chiral nucleon-nucleon interactions
• Nuclear structure effects in light muonic atoms
• Improved estimates of the nuclear structure corrections in $\mu$D
• Complex-energy approach to sum rules within nuclear density functional theory